We want the probability of at least 1 girl. Lets look at the probability of the opposite: all boys. There is a 1/2 chance at each birth that the child will be a boy, so for that to happen 3 times in a row, the odds are 1/2 * 1/2 * 1/2 = 1/8.
Any other possible composition of the family meets the condition laid down, so the odds of at least 1 girl are 1-1/8 = 7/8.